Dark matter and non-Newtonian gravity from General Relativity coupled to a fluid of strings

TL;DR

This paper presents an exact solution to Einstein's equations involving a point mass and a string fluid, revealing a modified gravity law at large distances that mimics dark matter effects and aligns with Milgrom's phenomenological law.

Contribution

It introduces a new exact solution coupling General Relativity with a string fluid, explaining galaxy rotation curves without dark matter and relating the critical acceleration to the Hubble parameter.

Findings

Near the string cloud limit, a 1/r correction to Newtonian gravity appears.

At large distances, the modified law matches Milgrom's phenomenological law.

The solution naturally explains the scale of Milgrom's critical acceleration.

Abstract

An exact solution of Einstein's field equations for a point mass surrounded by a static, spherically symmetric fluid of strings is presented. The solution is singular at the origin. Near the string cloud limit there is a $1/r$ correction to Newton's force law. It is noted that at large distances and small accelerations, this law coincides with the phenomenological force law invented by Milgrom in order to explain the flat rotation curves of galaxies without introducing dark matter. When interpreted in the context of a cosmological model with a string fluid, the new solution naturally explains why the critical acceleration of Milgrom is of the same order of magnitude as the Hubble parameter.